Exam 6: The Normal Distribution and Other Continuous Distributions

The amount of pyridoxine (in grams)in a multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams.What is the probability that a randomly selected vitamin will contain between 100 and 110 grams of pyridoxine?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is less than 1.15 is ________.

Instruction 6-2 The city manager of a large city believes that the number of reported accidents on any weekend has a normal distribution.She takes a sample of nine weekends and determines the number of reported accidents during each.The ordered array for this data is: 15,46,53,54,55,76,82,256,407. -Referring to Instruction 6-2,construct a normal probability plot.

When constructing a normal probability plot,the Z values are plotted on the vertical axis and the corresponding values of the variable are plotted on the horizontal axis.

Which of the following can be used to model the distribution of the values for a continuous random variable?

Instruction 6-7 A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15. -Referring to Instruction 6-7,which of the following is one of the properties required so that the binomial distribution can be used to compute the probability that no more than 2 computers will require repair on a given day?

Instruction 6-5 Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes. -Referring to Instruction 6-5,what is the probability that the time interval between two consecutive defective light bulbs will be between 10 and 35 minutes?

A catalogue company that receives the majority of its orders by telephone conducted a study to determine how long customers were willing to wait on hold before ordering a product.The length of time was found to be a random variable best approximated by an exponential distribution with a mean equal to 2.8 minutes.What is the probability that a randomly selected caller is placed on hold fewer than 7 minutes?

Patients arriving at an outpatient clinic follow an exponential distribution at a rate of 1 patient per hour.What is the probability that a randomly chosen arrival to be more than 2.5 hours?

Instruction 6-1 The manager of a surveying company believes that the average number of phone surveys completed per hour by her employees has a normal distribution.She takes a sample of 15 days' output from her employees and determines the average number of surveys per hour on these days.The ordered array for this data is: 10.0,10.1,10.3,10.5,10.7,11.2,11.4,11.5,11.7,11.8,11.8,12.0,12.2,12.2,12.5. -Referring to Instruction 6-1,the last standard normal quantile is ________.

Instruction 6-3 The number of column centimetres of classified advertisements appearing on Mondays in a certain daily newspaper is normally distributed with population mean 320 and population standard deviation 20 cm. -Referring to Instruction 6-3,a single Monday is chosen at random.State in which of the following ranges the number of column centimetres of classified advertisement is most likely to be

The amount of time necessary for assembly line workers to complete a product is a normal random variable with a mean of 15 minutes and a standard deviation of 2 minutes.The probability is ________ that a product is assembled in more than 19 minutes.

If we know that the length of time it takes a university student to find a parking space in the university car park follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute,find the probability that a randomly selected university student will take between 2 and 4.5 minutes to find a parking space in the car park.

Instruction 6-7 A company has 125 personal computers.The probability that any one of them will require repair on a given day is 0.15. -Referring to Instruction 6-7,which of the following is one of the properties required so that the binomial distribution can be used to compute the probability that no more than 2 computers will require repair on a given day?

If we know that the length of time it takes a university student to find a parking space in the university car park follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute,find the probability that a randomly selected university student will find a parking space in the car park in less than 3 minutes.

Times spent watching TV every week by primary school students follow an exponential distribution with mean 10 hours.The probability that a given primary school student spends more than 5 hours watching TV is ________.

As a general rule,one can use the normal distribution to approximate a binomial distribution whenever n(1-p)is at least 5.

Instruction 6-5 Suppose the time interval between two consecutive defective light bulbs from a production line has a uniform distribution over an interval from 0 to 90 minutes. -Referring to Instruction 6-5,the probability is 90% that the time interval between two consecutive defective light bulbs will fall between which two values that are the same distance from the mean?

The probability that a standard normal random variable,Z,is between 1.00 and 3.00 is 0.1574.

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1.The probability that Z is less than -2.20 is ________.